Solve the following systems of simultaneous linear equations by the elimination method

$\dfrac{x}{6} = y - 6$

$\dfrac{3x}{4} = 1 + y$

Given,

$\dfrac{x}{6} = y - 6$ …….(i)

$\dfrac{3x}{4} = 1 + y$ ……(ii)

Subtracting eq. (i) from (ii) we get,

$\Rightarrow \dfrac{3x}{4} - \dfrac{x}{6} = 1 + y - (y - 6) \\[1em] \Rightarrow \dfrac{9x - 2x}{12} = 7 \\[1em] \Rightarrow \dfrac{7x}{12} = 7 \\[1em] \Rightarrow x = \dfrac{7 \times 12}{7} \\[1em] \Rightarrow x = 12.$

Substituting value of x in eq. (i) we get,

$\Rightarrow \dfrac{12}{6} = y - 6 \\[1em] \Rightarrow 2 = y - 6 \\[1em] \Rightarrow y = 2 + 6 = 8.$

Hence, x = 12 and y = 8.